Exact mean-field theory of ionic solutions: non-Debye screening

From Solvent-Free to Dilute Electrolytes: Essential Components for a Continuum Theory

“…20,30,46 Eqs. 4 gives rise to a richer picture of bulk and interfacial behavior, that is consistent with the picture arising in recent experimental and numerical studies.…”

Pseudolattice Theory of Ionic Liquids

“…On the basis of this structural model of ionic solutions, the thermodynamic properties of extremely dilute ionic solutions have been successfully understood including surface properties (see, for example, the classic books of Harned and Owen (Harned & Owen, 1958) and of Robinson and Stokes (Robinson & Stokes, 1959) for a detailed overview of classical theory of electrolyte solutions). Nowadays, meanfield, Poisson Boltzmann (PB) equation-based theories which provide simple, elegant expression that can be applied in practical situations continue to be the most frequently used to describe ionic fluids, despite the huge amount of contributions to the field of ionic solutions reported during the last century, that include different extensions of the DebyeHückel formalism, integral equation techniques, field theory studies and computer simulation results (for a review, see (Varela et al, 2003) and references therein). Indeed, the mean-field approach is very successful in describing qualitatively (and usually also quantitatively) experiments and simulation in Coulomb systems because every ion interacts with many other ions simultaneously.…”

“…These inhomogeneities in the distribution of charge in the bulk solution are associated to local electroneutrality and they provide the structural tools for the understanding of these systems in the dilute concentration regime. Moreover, it is now well-stated that the mean-field Poisson-Boltzmann formalism can be extended to regions where it should not be qualitatively valid (Varela et al 2003;Kjellander & Mitchell, 1992;Kjellander & Mitchell, 1994;Attard, 1993;McBride et al, 1998;Varela et al 1998;Varela et al 1999,a,b). Indeed, an effective, formally exact mean-field theory can be defined where the screening length and charges are renormalized from their bare values (Varela et al, 2003).…”

“…Moreover, it is now well-stated that the mean-field Poisson-Boltzmann formalism can be extended to regions where it should not be qualitatively valid (Varela et al 2003;Kjellander & Mitchell, 1992;Kjellander & Mitchell, 1994;Attard, 1993;McBride et al, 1998;Varela et al 1998;Varela et al 1999,a,b). Indeed, an effective, formally exact mean-field theory can be defined where the screening length and charges are renormalized from their bare values (Varela et al, 2003). Using these extensions, the Poisson-Boltzmann formalism can be extended in order to treat solutions of very high ionic concentrations for which the interionic correlations must be considered.…”

A modified Poisson-Boltzmann approach to homogeneous ionic solutions

“…Increased computer power and speed now enables ever more models to be accurately simulated and more complex theoretical analysis to be evaluated numerically. Many excellent reviews have appeared over the years and we list a few of the most recent [3][4][5][6][7][8][9].…”